which appears to us to have any degree of probability, however small, must at least be possible. But the axiom, taken in this sense, is surely false. It would be superfluous to give instances of this to a mathematician.
'If it should be said that conceiving a proposition to be true means, neither barely to understand the meaning of the proposition, nor the giving any degree of assent to it, I would be glad to know what it really does mean. For I am at a loss to know what power of the understanding we mean by the conceiving a proposition to be true, if it is neither simple apprehension, by which we barely understand the meaning of a proposition, nor judgment, by which we assent to the proposition or dissent from it. I know of no power of the understanding intermediate between these two. And if there is none, I think the axiom must be false.
'There are many propositions which, by the faculties God has given us, we perceive to be not only true, but necessarily true; and the contradictions of these must be impossible. So that our knowledge of what is impossible keeps pace with our knowledge of necessary truth.
'By our senses and our memory, by testimony and other means, we have the certain knowledge of many truths which we do not perceive to be necessary; their contraries therefore may be possible for aught we know. But we know that whatever is true, whether necessary or not, is possible. Our knowledge therefore of what is possible keeps pace with our knowledge of truth, whether contingent or necessary. Beyond this, I am afraid our knowledge of what is possible is conjectural. And although we are apt to think everything to be possible which we do not perceive to be impossible, yet in this we may be greatly deceived. You know well, sir, that mathematics affords many instances of impossibilities in the nature of things, which no man would have dreamed of or believed, until they were discovered by accurate and subtle reasoning. Perhaps if we were able to reason demonstratively to as great an extent in other subjects as in mathematics, we might discover many things to be impossible which we now take to be possible. We are apt to think it possible that God might have made an universe of sensible and rational creatures, into which neither natural nor moral Evil should ever enter. It may be so for what I know. But how are you certain that this
